dedication dithering

I have a painting by bill bissett that hangs over my bed:

It was bought directly from bill, in bill's apartment, and has a dedication from bill written on the back.

The dedication is not to me. It's to my ex, who bought it when I wasn't present. When he left me, at the last dividing-up-our-stuff session, he glanced at the painting (then gracing the living room) and said, "You want that? You always liked it."

I was astonished. "Sure, I'd love to have it."

"Keep it." And that was that.

What do dedications and autographs mean? I used to think they were souvenirs, reminders that the you got to meet the someone who had created the something you liked so much. To discard the signed something would be to discard the appreciation that led you to seek out the signing in the first place.

I've learned it hasn't always been that way. I've seen someone use a dedication or autograph to steal a book from someone else ("Oh, when he signed it he put it to me, not you. I guess he misunderstood. I'll get you another copy"), to make the fake authentic, to commodify something as insignificant as a paper serviette.

Above all, in the downloadable age, what does a signature mean anymore? And what's to sign if nothing is in a  version one can touch? I've heard stories of people getting their iPods signed, but I've never known anyone who's had this done, and it seems silly to get something signed when you'll be lucky if you can even get it to work in twenty years' time.

So what's really of value? The signature or the signed?